This invention was made for the purpose of constructing a flexible conduit element, especially for the exhaust systems of combustion engines in vehicles, and in particular, the invention is directed to helically or annularly corrugated metal bellows equipped with cylindrical end fittings and a metal hose which is located coaxially inside the bellows, where the outside diameter of the metal hose is smaller than the free (smallest) inside diameter of the bellows and the ends of the metal hose are lying inside the end fittings of the bellows, are flush with those fittings, and are fixed to them, with at least one hollow cylindrical element made of metal wire being arranged between the bellows and the metal hose. In this well-known type of conduit element, a braided hose is used as the metal wire element arranged between the bellows and the metal hose in order to improve the damping of vibrations. At least one of the ends of the braided hose is fixed inside an end fitting of the corresponding bellows. The damping effect of this design, however, was found to be quite low since the braided hose lies loosely in the cavity between the bellows and the metal hose and is in contact only with the bellows in order to have a damping effect. The damping effect is therefore subject to accidental conditions in the operation of the conduit element. Furthermore, the braided hose requires the fixing of at least one of its ends. In addition thereto, the braided hose causes a comparably high material consumption due to its design. Finally, the braided hose is particularly incapable of keeping the metal hose in a radially constant position inside the bellows. Under unfavorable operating conditions the metal hose may collide with the interior walls of the bellows. Conventionally, additional elements are to be packed into the cavity between the metal hose and the bellows to avoid such effects. As a consequence, the manufacturing costs of such a conventional conduit element are high and its installation is difficult.